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Five people were playing a board gave in which to start the game one had to roll a die and obtain either a one or

Five people were playing a board gave in which to start the game one had to roll a die and obtain either a one or a six dots.It took them respectively 5,3, 1, 4, and 2 rounds, to start the game.If we assume that the die that they used was quite fair and that the prior probability q of getting either one or a six dots followed BETA (2,7) distribution, find the Bayes estimate of q assuming the squared error loss.

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